Simple & Compound Interest
Delhi Police Exam
1. What is Interest?
When money is borrowed or invested, the extra amount paid or earned for using that money over time is called Interest.
Simple Interest (S.I.)
Compound Interest (C.I.)
Key Terms:
Interest → The extra money paid for using borrowed money
Principal (P) → The original amount of money
Rate (R) → The percentage of interest charged per year
Time (T) → Duration in years
2. Simple Interest (S.I.)
S.I. = (P × R × T) / 100
Total Amount (A) = P + S.I.
Example:
If ₹5000 is borrowed at 10% per annum for 2 years:
S.I. = (5000 × 10 × 2) / 100 = ₹1000
Total Amount = 5000 + 1000 = ₹6000
Key Points:
| Year | Interest (₹) | Total (₹) |
|---|---|---|
| 1st Year | 500 | 5500 |
| 2nd Year | 500 | 6000 |
• Interest is same every year
• Grows linearly with time
3. Compound Interest (C.I.)
In Compound Interest, interest is added to the principal after every time period — so the next period's interest is calculated on the new amount (interest on interest).
A = P(1 + R/100)T
C.I. = A - P
Example:
If ₹5000 is invested at 10% p.a. for 2 years (compounded annually):
A = 5000(1 + 10/100)2 = 5000 × 1.21 = ₹6050
So, C.I. = 6050 - 5000 = ₹1050
4. Difference Between S.I. and C.I.
| Basis | Simple Interest | Compound Interest |
|---|---|---|
| Definition | Interest on principal only | Interest on principal + previous interest |
| Formula | (P×R×T)/100 | P(1 + R/100)T – P |
| Growth | Linear | Exponential |
| Interest Amount | Same every year | Increases every year |
| Example | ₹1000, ₹1000, ₹1000 | ₹1000, ₹1100, ₹1210 |
5. Compound Interest (for Different Periods)
Half-yearly
A = P(1 + R/(2×100))2T
Quarterly
A = P(1 + R/(4×100))4T
Example:
₹8000 at 10% p.a. for 1 year, compounded half-yearly
A = 8000(1 + 10/200)2 = 8000(1.05)2 = 8000 × 1.1025 = ₹8820
C.I. = 8820 - 8000 = ₹820
6. Short Tricks & Relations
| Concept | Formula / Shortcut |
|---|---|
| If Time = 2 years | C.I. = S.I. + (S.I. on S.I. for 1 year) |
| Difference between C.I. and S.I. (2 years) | P × (R2) / 1002 |
| When P and R are same | C.I. > S.I. |
| Double/Triple Money | Use formula 2P = P(1 + R/100)T |
Example:
At what rate will ₹500 double in 10 years (C.I.)?
2 = (1 + R/100)10
(1 + R/100) = 21/10 ≈ 1.0718
So, R ≈ 7.18%
7. Important Terms
| Term | Meaning |
|---|---|
| Principal (P) | Original amount invested/borrowed |
| Rate (R) | Percentage of interest per year |
| Time (T) | Period in years |
| Amount (A) | Total sum after interest |
| Interest | Extra money earned or paid |
8. Real-Life Analogy
Imagine depositing money in a bank:
Simple Interest
The bank gives you same interest every year
Compound Interest
The bank gives you interest on your previous interest
With Compound Interest, your money grows faster — like a snowball effect!
9. Common Delhi Police / SSC Exam Facts
Formula for S.I. = (P × R × T) / 100
Formula for C.I. = P(1 + R/100)T – P
C.I. is always greater than or equal to S.I.
When time = 1 year → S.I. = C.I.
Difference (for 2 years) = P × R2 / 1002
For half-yearly compounding → R = R/2, T = 2T
10. Quick Recap
| Concept | Summary |
|---|---|
| Principal | Original money |
| Interest | Extra money earned or paid |
| Simple Interest | Fixed each year |
| Compound Interest | Increases each year |
| Relation | C.I. ≥ S.I. |
| Main Formula | A = P(1 + R/100)T |
You've completed Simple & Compound Interest Concepts!
Courage Tip: Remember the key formulas for Simple and Compound Interest calculations. Practice the difference between C.I. and S.I. for 2-3 years, which is frequently asked in Delhi Police exams.
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